Introduction to and Historical Overview of Quantum Logics Speaker(s): Alexander Wilce
Abstract: Introductory lecture summary:
1. Finite dimensional hilbert spaces and (complemented) modular lattices; infinitedimensional hilbert spaces and orthomodularity.
2. von Neumann's QL; von NeumannBirkhoff (briefly!); reconstruction of QM from P(H)
3. Mackey's programme; some early axiomatics (e.g., Zierler); QLs as OMPs + orderdetermining sets of states
4. Piron's Theorem; some discussion of Piron's axioms
5. Keller's examples (maybe just a mention, though I'd like to indicate how they come up); Soler's theorem (just the statement)
6. Abstract OMLs; Greechie Diagrams and the Loop Lemma; brief mention of Harding's results on decompositions
7. Tensor products (the FR example, showing OMLs not stable under tensor products); orthoalgebras.
8. Orthoalgebras from test spaces
Date: 17/07/2005  2:00 pm
